Final answer:
To determine if the box will slide down the inclined conveyor, we compare the force of friction with the force pulling the box down the incline. Using the formula Ffriction <= μs * Fnormal, where μs is the static coefficient of friction and Fnormal is the normal force, we can calculate the static friction force. If the force pulling the box down is lesser than the static friction force, the box will not slide down.
Step-by-step explanation:
To determine if the box will slide down the inclined conveyor, we need to compare the force of friction with the force pulling the box down the incline. The formula we can use is Ffriction <= μs * Fnormal, where μs is the static coefficient of friction and Fnormal is the normal force.
The normal force is equal to the weight of the box, which is the mass of the box times the acceleration due to gravity. Given that the box has a weight of 500 lb, we can convert this to kilograms by dividing by the conversion factor of 2.205 lb/kg. The acceleration due to gravity is approximately 9.8 m/s².
Plugging in the values, we find that the static friction force is equal to 500 lb * 2.205 lb/kg * 9.8 m/s² * 0.40 = 428.08 N. Since the force pulling the box down the incline is lesser than the static friction force, the box will not slide down.